Tackling the target matrix definition in MIMO Random Vibration Control testing

Nowadays the advantages of performing Multiple-Input-Multiple-Output (MIMO) Random Vibration Control tests are widely accepted by the environmental engineering community. However their practice still needs to grow because of the high degree of expertise needed to perform these tests. The challenges start even before the actual test, with the definition of a realizable full Spectral Density Matrix as test reference (the control target). Defining this matrix with no a-priori knowledge of the off-diagonal terms is challenging: this operation must guarantee that the target can have a physical meaning. This is translated in the algebraic constraint that the target matrix needs to be positive (semi)-definite. On the other hand the requirements of any Random Vibration Control test are Power Spectral Densities (PSDs), representative for the acceleration operational levels at the control locations. In defining the reference matrix, the main challenge is then to guarantee a physically realizable full target spectral density matrix that has fixed PSD terms. The purpose of this work is to show the capabilities and the limitations of different state-of-the-art and more innovative solutions for the MIMO Random Vibration Control target definition in order to aim to a well-defined automatic procedure to be included in the standard practice.